Ace Low Straight Poker

1. Ace Low Straight Poker
2. Poker Straight Hand
3. Small Straight In Poker

In poker, a straight is made when we hold 5 cards all of consecutive rank, for example, 56789. Aces can be both high and low for the purposes of creating a straight, but the Ace must either appear at the beginning or end of the hand’s structure. Question 2: Which straight wins in poker? The highest possible straight flush, and the best hand in poker, is an ace high straight flush, also known as a royal flush A “royal flush” consists of a straight from ten to the ace with all five cards of the same suit. A royal flush is exceptionally rare and is therefore the most coveted hand in poker. Can Ace Be Low In Poker Straight. Company Registration Number C50978. 2.3 Dazzletag Entertainment Limited is licensed to provide remote casino facilities to customers in Great Britain. I am studying probability at the moment, and find myself often having to deal with calculating the probability of poker hands, and thus have to be crystal clear on the definition of poker hands. A straight is supposed to be any sequence of 5 cards. However, the following hands are excluded from being considered straights: K, A, 2, 3, 4; Q, K, A.

Lowball or low poker is a variant of poker in which the normal ranking of hands is inverted. Several variations of lowball poker exist, differing in whether aces are treated as high cards or low cards, and whether straights and flushes are used.

Low-poker ranking[edit]

Lowball inverts the normal ranking of poker hands. There are three methods of ranking low hands, called ace-to-five low, deuce-to-seven low, and ace-to-six low. The 'ace-to-five' method is most common. A sub-variant within this category is 'high-low poker', in which the highest and lowest hands split the pot, with the highest hand taking any odd chips if the pot does not divide equally. Sometimes straights and/or flushes count in determining which hand is highest but not in determining which hand is lowest, being reckoned as a no-pair hand in the latter instance, so that a player with such a holding can win both ways and thus take the entire pot.

Lowball variants[edit]

The most popular forms of lowball are ace-to-five lowball (also known as California lowball), and deuce-to-seven lowball (also known as Kansas City lowball). Ace-to-five lowball gets its name because the best hand at that form is 5-4-3-2-A. In ace-to-five lowball straights and flushes do not prevent a hand from being low. You win by simply having the five lowest cards. Deuce-to seven lowball gets its name because the best hand at that form is 7-5-4-3-2 (not of the same suit).^[1]

Ace-to-five[edit]

Ace-to-five low is the most common method for evaluating low hands in poker, nearly universal in U.S. casinos, especially in high-low split games.

As in all low hand games, pairs count against the player. That is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or three of a kind, etc. No-pair hands are compared starting with the highest-ranking card, just as in high poker, except that the high hand loses. In ace-to-five low, straights and flushes are ignored, and aces play as the lowest card.

For example, the hand 8-5-4-3-2 defeats 9-7-6-4-3, because eight-high is lower than nine-high. The hand 7-6-5-4-3 defeats both, because seven-high is lower still, even though it would be a straight if played for high. Aces are low, so 8-5-4-3-A defeats 8-5-4-3-2. Also, A-A-9-5-3 (a pair of aces) defeats 2-2-5-4-3 (a pair of deuces), but both of those would lose to any no-pair hand such as K-J-8-6-4. In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): 3-3-6-4-2 defeats 3-3-6-5-A.

This is called ace-to-five low because the lowest (and therefore best) possible hand is 5-4-3-2-A, called a 'wheel'. The next best possible hand is 6-4-3-2-A, followed by 6-5-3-2-A, 6-5-4-2-A, 6-5-4-3-A, 6-5-4-3-2, 7-4-3-2-A, 7-5-3-2-A, etc.

When speaking, low hands are referred to by their highest-ranking card or cards. Any nine-high hand can be called 'a nine', and is defeated by any 'eight'. Two cards are frequently used: the hand 8-6-5-4-2 can be called 'an eight-six' and will defeat 'an eight-seven' such as 8-7-5-4-A.

Another common notation is calling a particular low hand 'smooth' or 'rough.' A smooth low hand is one where the remaining cards after the highest card are themselves very low; a rough low hand is one where the remaining cards are high. For instance, 8-7-6-3-A would be referred to as a 'rough eight,' but 8-4-3-2-A would be referred to as a 'smooth eight.' Some players refer to a hand containing a 4-3-2-A (in ace-to-five low or ace-to-six low) or a 5-4-3-2 (in deuce-to-seven low) as a 'nut' (thus, in ace-to-five or ace-to-six, a 7-4-3-2-A would be called a 'seven nut').

High-low split games with ace-to-five low are usually played cards speak, that is, without a declaration. Frequently a qualifier is required for low (typically 8-high or 9-high). Some hands (particularly small straights and flushes) may be both the low hand and the high hand, and are particularly powerful (or particularly dangerous if they are mediocre both ways). Winning both halves of the pot in a split-pot game is called 'scooping' or 'hogging' the pot. The perfect hand in such a game is called a 'steel wheel', 5-4-3-2-A of one suit, which plays both as perfect low and a straight flush high. Note that it is possible—though unlikely—to have this hand and still lose money. If the pot has three players, and one other player has a mixed-suit wheel, and a third has better straight flush, the higher straight flush wins the high half of the pot, and the two wheels split the low half, hence the steel wheel wins only a quarter of a three-way pot.

Ace-to-five lowball, a five-card draw variant, is often played with a joker added to the deck. The joker plays as the lowest card not already present in the hand (in other words, it is a wild card): 7-5-4-Joker-A, for example, the joker plays as a 2. This can cause some interesting effects for high-low split games. Let's say that Alice has 6-5-4-3-2 (called a 'straight six')--a reasonably good hand for both high and low. Burt has Joker-6-5-4-3. By applying the rule for wild cards in straights, Burt's joker plays as a 7 for high, giving him a seven-high straight to defeat Alice's six-high straight. For low, the joker plays as an ace—the lowest card not in Burt's hand—and his hand also defeats Alice for low, because his low hand is 6-5-4-3-A, lower than her straight six by one notch. Jokers are very powerful in high-low split games.

Wheel[edit]

A wheel or bicycle is the poker hand 5-4-3-2-A, regardless of suit, which is a five-high straight, the lowest-ranking of the straights.

In ace-to-five low poker, where aces are allowed to play as low and straights and flushes do not count against a hand's 'low' status, this is the best possible hand. In high/low split games, it is both the best possible low hand and a competitive high hand. The best deuce-to-seven low hand, 7-5-4-3-2, is also sometimes called 'the wheel'.

Ace-to-six[edit]

Ace-to-six low is not as commonly used as the ace-to-five low method, but it is common among home games in the eastern region of the United States, some parts of the mid-west, and also common in the United Kingdom (it is the traditional ranking of London lowball, a stud poker variant).

As in all lowball games, pairs and trips are bad: that is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or trips, etc. No-pair hands are compared starting with the highest-ranking card, just as in high poker, except that the high hand loses. In ace-to-six low, straights and flushes are accounted for (as compared to Ace-to-five) and count as high (and are therefore bad), and aces play as the lowest card.

For example, the hand 8-5-4-3-2 defeats 9-7-6-4-3, because eight-high is lower than nine-high. The hand 7-6-5-4-2 defeats both, because seven-high is lower still. The hand 7-6-5-4-3 would lose, because it is a straight. Aces are low, so 8-5-4-3-A defeats 8-5-4-3-2. Also, A-A-9-5-3 (a pair of aces) defeats 2-2-5-4-3 (a pair of deuces), but both of those would lose to any no-pair hand such as K-J-8-6-4. In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): 3-3-6-4-2 defeats 3-3-6-5-A.

It is called ace-to-six low because the best possible hand is 6-4-3-2-A (also known as a Chicago Wheel or a 64), followed by 6-5-3-2-A, 6-5-4-2-A, 6-5-4-3-A, 7-4-3-2-A, 7-5-3-2-A, etc.

When speaking, low hands are referred to by their highest-ranking card or cards. Any nine-high hand can be called 'a nine', and is defeated by any 'eight'. Two cards are frequently used: the hand 8-6-5-4-2 can be called 'an eight-six' and will defeat 'an eight-seven' such as 8-7-5-4-A.

A wild card plays as whatever rank would make the lowest hand. Thus, in 6-5-Joker-2-A, the joker plays as a 3, while in Joker-5-4-3-2 it would play as a 7 (an ace or six would make a straight).

High-low split games with ace-to-six low are usually played with a declaration.

Deuce-to-seven[edit]

Deuce-to-seven low is often called Kansas City lowball (the no-limit single-draw variation) or just 'low poker'. It is almost the direct opposite of standard poker: high hand loses. It is not as commonly used as the ace-to-five low method.

As in all lowball games, pairs and trips are bad: that is, any hand with no pair defeats any hand with a pair; one pair hands defeat two pair or trips, etc. No-pair hands are compared starting with the highest-ranking card, just as in high poker, except that the high hand loses. In deuce-to-seven low, straights and flushes count as high (and are therefore bad). Aces are always high (and therefore bad).

For example, the hand 8-5-4-3-2 defeats 9-7-6-4-3, because eight-high is lower than nine-high. The hand 7-6-5-4-2 defeats both, because seven-high is lower still. The hand 7-6-5-4-3 would lose, because it is a straight. Aces are high, so Q-8-5-4-3 defeats A-8-5-4-3. In the rare event that hands with pairs tie, kickers are used just as in high poker (but reversed): 3-3-6-4-2 defeats 3-3-6-5-2.

Since the ace always plays high, A-5-4-3-2 (also called the Nut Ace) is not considered a straight; is simply ace-high no pair (it would therefore lose to any king-high, but would defeat A-6-4-3-2).

The best possible hand is 7-5-4-3-2 (hence the name deuce-to-seven low), followed by 7-6-4-3-2, 7-6-5-3-2, 7-6-5-4-2, 8-5-4-3-2, 8-6-4-3-2, etc. Hands are sometimes referred to by their absolute rank, e.g. 7-5-4-3-2 (#1, said 'number one', see table).

When speaking, low hands are referred to by their highest-ranking card or cards. Any nine-high hand can be called 'a nine', and is defeated by any 'eight'. Two cards are frequently used: the hand 8-6-5-4-2 can be called 'an eight-six' and will defeat 'an eight-seven' such as 8-7-5-4-2.

Another common notation is calling a particular low hand 'smooth' or 'rough.' A smooth low hand is one where the remaining cards after the highest card are themselves very low; a rough low hand is one where the remaining cards are high. For instance, 8-7-6-4-2 would be referred to as a 'rough eight,' but 8-5-4-3-2 would be referred to as a 'smooth eight.'

Wild cards are rarely used in deuce-to-seven games, but if used they play as whatever rank would make the lowest hand. Thus, in 7-6-Joker-3-2, the joker plays as a 4, while in Joker-5-4-3-2 it would play as a 7 (a six would make a straight).

High-low split games with deuce-to-seven low are usually played with a declaration.

See also[edit]

References[edit]

1. ^'Low Ball Poker Variants'. WorldSeriesOfPoker.com. Retrieved 2009-09-27.

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In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Frequency of 5-card poker hands

The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. (The frequencies given are exact; the probabilities and odds are approximate.)

The nCr function on most scientific calculators can be used to calculate hand frequencies; entering ​nCr​ with ​52​ and ​5​, for example, yields as above.

The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.

When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.

Note that since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. For example, the hand 3♣ 7♣ 8♣ Q♠ A♠ is identical to 3♦ 7♦ 8♦ Q♥ A♥ because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.

The number of distinct poker hands is even smaller. For example, 3♣ 7♣ 8♣ Q♠ A♠ and 3♦ 7♣ 8♦ Q♥ A♥ are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand when there are more cards to come. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands.

Poker Straight Hand

Derivation of frequencies of 5-card poker hands

of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set. See also: sample space and event (probability theory).

• Straight flush — Each straight flush is uniquely determined by its highest ranking card; and these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. Thus, the total number of straight flushes is:
  • Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is

    or simply . Note: this means that the total number of non-Royal straight flushes is 36.

• Four of a kind — Any one of the thirteen ranks can form the four of a kind by selecting all four of the suits in that rank. The final card can have any one of the twelve remaining ranks, and any suit. Thus, the total number of four-of-a-kinds is:

• Full house — The full house comprises a triple (three of a kind) and a pair. The triple can be any one of the thirteen ranks, and consists of three of the four suits. The pair can be any one of the remaining twelve ranks, and consists of two of the four suits. Thus, the total number of full houses is:

• Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:

• Straight — The straight consists of any one of the ten possible sequences of five consecutive cards, from 5-4-3-2-A to A-K-Q-J-10. Each of these five cards can have any one of the four suits. Finally, as with the flush, the 40 straight flushes must be excluded, giving:

• Three of a kind — Any of the thirteen ranks can form the three of a kind, which can contain any three of the four suits. The remaining two cards can have any two of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of three-of-a-kinds is:

Small Straight In Poker

• Two pair — The pairs can have any two of the thirteen ranks, and each pair can have two of the four suits. The final card can have any one of the eleven remaining ranks, and any suit. Thus, the total number of two-pairs is:

• Pair — The pair can have any one of the thirteen ranks, and any two of the four suits. The remaining three cards can have any three of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of pair hands is:

• No pair — A no-pair hand contains five of the thirteen ranks, discounting the ten possible straights, and each card can have any of the four suits, discounting the four possible flushes. Alternatively, a no-pair hand is any hand that does not fall into one of the above categories; that is, any way to choose five out of 52 cards, discounting all of the above hands. Thus, the total number of no-pair hands is:

• Any five card poker hand — The total number of five card hands that can be drawn from a deck of cards is found using a combination selecting five cards, in any order where n refers to the number of items that can be selected and r to the sample size; the '!' is the factorial operator:

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